Identify, graph and state the symmetries for each polar equation.
r=9 cos (5 theta)
r=2 cos theta

Both equation are symmetric about the x-axis.

Step-by-step explanation:

If (r,θ) can be replaced by (r,-θ),then the graph is symmetric about the x-axis.

If (r,θ) can be replaced by (-r,-θ),then the graph is symmetric about the y-axis.

If (r,θ) can be replaced by (-r,θ),then the graph is symmetric about the origin.

The given equation is

Replace the value of (r,θ) by (r,-θ).

It is symmetric about the x-axis.

Replace the value of (r,θ) by (-r,-θ).

It is not symmetric about the y-axis.

Replace the value of (r,θ) by (-r,θ).

It is not symmetric about the origin.

Therefore the first equation is symmetric about the x-axis.

The given equation is

Replace the value of (r,θ) by (r,-θ).

It is symmetric about the x-axis.

Replace the value of (r,θ) by (-r,-θ).

It is not symmetric about the y-axis.

Replace the value of (r,θ) by (-r,θ).

It is not symmetric about the origin.

Therefore the second equation is symmetric about the x-axis.

answer: 1, 3 and 5 are correct

step-by-step explanation: